I absolutely disagree. Conservatives as a whole absolutely do have empathy...
...but the issue's deeper than a simple question.
The smaller issue is that those who lack empathy - as Ayn Rand certainly did - are significantly more likely to be conservative. The bigger issue by far is that conservatives are being taught and pressured by their own to believe that empathy for the less fortunate is a bad thing, that helping the poor get a leg up in life is actually hurting the poor, teaching the poor to be lazy.
The same thing could be seen in any dictatorship: people are the same all over the world, but when the people of a nation are being told a thing and do not for whatever reason get the other side of the story, they're more likely to believe that thing. America's conservatives have been taught to believe that liberals and the poor want to destroy America, to destroy the American way of life...and any conservative who happens to agree with any liberal point of view is seen as a traitor, a turncoat.
So while conservatives certainly do have empathy for the less fortunate, most of them are afraid of showing that empathy (or of showing agreement with any liberal point of view) for fear of being seen by their fellow conservatives as traitors, as RINO's or CINO's. I'm not trying to make any comparisons to Nazism, but Goering hit the nail on the head in his famous quote:
"Naturally the common people don't want war: Neither in Russia, nor in England, nor for that matter in Germany. That is understood. But, after all, IT IS THE LEADERS of the country who determine the policy and it is always a simple matter to drag the people along, whether it is a democracy, or a fascist dictatorship, or a parliament, or a communist dictatorship. Voice or no voice, the people can always be brought to the bidding of the leaders. That is easy. All you have to do is TELL THEM THEY ARE BEING ATTACKED, and denounce the peacemakers for lack of patriotism and exposing the country to danger. IT WORKS THE SAME IN ANY COUNTRY."
How many times have we heard the conservative politicians and pundits claim that America is under attack from liberals? How many times have we seen the conservative elite reject any conservative politician for even considering a negotiated compromise on major issues facing America?
It's not a matter of conservatives lacking empathy. It's a matter of conservatives being pressured to believe that which is not true.